The date is listed based on her wedding and child birth dates and when she died in childbirth at around the age of 20 in 1736. Her Wikipedia article is here.

Louise Diane;s dress looks somewhat Louis XIV - no panniers or gushing engageantes and a somewhat built up coiffure. But it is not a mantua and she is not wearing a Fontanges headdress. The notched sleeves and minimum engageantes were stylish durinh the early Louis XV period - marking this as transitional court dress.